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Permutation : Rearranging Letters of a Word

Question 5

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

(1)

(2) 3!*3!

(3)
(4)

(5) 72

Correct Answer is - Choice 4

Explanation

ABACUS is a 6 letter word with 3 of the letters being vowels.

If the 3 vowels have to appear together as stated in the question, then there will 3 consonants and a set of 3 vowels grouped together.

One group of 3 vowels and 3 consonants are essentially 4 elements to be rearranged.

The number of possible rearrangements is 4!

The group of 3 vowels contains two 'a's and one 'u'.

The 3 vowels can rearrange amongst themselves in ways as the vowel "a" appears twice.

Hence, the total number of rearrangements in which the vowels appear together are

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